The effect of the cubic anisotropy on the angular dependence of the exchange bias

Summary form only given. Exchange bias effect arises from the direct exchange interaction at the interface between the ferromagnetic (FM) and antiferromagnetic (AFM) systems such as bilayers and nanoparticles. In recent years, this effect has been extensively studied for its important applications to the magnetoresistance sensors and spin valves [1]. Among these studies, the angular dependence of exchange bias (ADEB) is an important aspect of the exchange bias effect. It can provide an independent test for the validity of the existing models. Additionally, the types, strengths and orientations of the anisotropies in exchange-biased systems can also be detected by fitting the experimental measurements of ADEB with theoretically calculated ones [2]. Recently, a jump phenomenon in the ADEB has been confirmed both experimentally and theoretically [3-5]. This new feature is important to maximize the exchange bias field for optimizing the designs of the involved devices. However, most works mentioned above concentrate only on the uniaxial anisotropy in the systems. The influence of another common anisotropy, cubic anisotropy, on the ADEB has rarely been involved. In this work, the effect of the cubic anisotropy on the ADEB has been studied in detail. When the external field is absent at the initial magnetization stage, the bilayers will be in mono-stable, bi-stable, tri-stable and quadric-stable states, which are dependent on the competition among the unidirectional, uniaxial and cubic anisotropies of the bilayers. The magnitude of the cubic anisotropy will significantly affect the exchange bias by making a transition among these initial states. This transition induces a significant change in the shape of the ADEB. It is found that the jump phenomenon is still existent in the angular dependence of the exchange bias when the cubic anisotropy is included in the bilayers. Both the exchange bias field and the coercivity are larger in the magnitude at the points of the jumps.- At some jumping points, the maximum values of HEB and HC can even be observed. We hope that our investigations will be useful to gain a better understanding of the effect of the cubic anisotropy on the exchange bias.